Regularity for convex viscosity solutions of Lagrangian mean curvature equation
We show that convex viscosity solutions of the Lagrangian mean curvature equation are regular if the Lagrangian phase has Hölder continuous second derivatives.
math.AP↗
arXiv subjects
Ravi Shankar
Publications and source records attributed to Ravi Shankar.
A Comparative Study of Data Augmentation Techniques for Deep Learning Based Emotion Recognition
Automated emotion recognition in speech is a long-standing problem. While early work on emotion recognition relied on hand-crafted features and simple classifiers, the field has now embraced end-to-end feature learning and classification using deep neural networks. In parallel to these models, researchers have proposed several data augmentation techniques to increase the size and variability of existing labeled datasets. Despite many seminal contributions in the field, we still have a poor understanding of the interplay between the network architecture and the choice of data augmentation. Moreover, only a handful of studies demonstrate the generalizability of a particular model across multiple datasets, which is a prerequisite for robust real-world performance. In this paper, we conduct a comprehensive evaluation of popular deep learning approaches for emotion recognition. To eliminate bias, we fix the model architectures and optimization hyperparameters using the VESUS dataset and then use repeated 5-fold cross validation to evaluate the performance on the IEMOCAP and CREMA-D datasets. Our results demonstrate that long-range dependencies in the speech signal are critical for emotion recognition and that speed/rate augmentation offers the most robust performance gain across models.
eess.AS↗
A Diffeomorphic Flow-based Variational Framework for Multi-speaker Emotion Conversion
This paper introduces a new framework for non-parallel emotion conversion in speech. Our framework is based on two key contributions. First, we propose a stochastic version of the popular CycleGAN model. Our modified loss function introduces a Kullback Leibler (KL) divergence term that aligns the source and target data distributions learned by the generators, thus overcoming the limitations of sample wise generation. By using a variational approximation to this stochastic loss function, we show that our KL divergence term can be implemented via a paired density discriminator. We term this new architecture a variational CycleGAN (VCGAN). Second, we model the prosodic features of target emotion as a smooth and learnable deformation of the source prosodic features. This approach provides implicit regularization that offers key advantages in terms of better range alignment to unseen and out of distribution speakers. We conduct rigorous experiments and comparative studies to demonstrate that our proposed framework is fairly robust with high performance against several state-of-the-art baselines.
eess.AS↗
Knowledge Graph - Deep Learning: A Case Study in Question Answering in Aviation Safety Domain
In the commercial aviation domain, there are a large number of documents, like, accident reports (NTSB, ASRS) and regulatory directives (ADs). There is a need for a system to access these diverse repositories efficiently in order to service needs in the aviation industry, like maintenance, compliance, and safety. In this paper, we propose a Knowledge Graph (KG) guided Deep Learning (DL) based Question Answering (QA) system for aviation safety. We construct a Knowledge Graph from Aircraft Accident reports and contribute this resource to the community of researchers. The efficacy of this resource is tested and proved by the aforesaid QA system. Natural Language Queries constructed from the documents mentioned above are converted into SPARQL (the interface language of the RDF graph database) queries and answered. On the DL side, we have two different QA models: (i) BERT QA which is a pipeline of Passage Retrieval (Sentence-BERT based) and Question Answering (BERT based), and (ii) the recently released GPT-3. We evaluate our system on a set of queries created from the accident reports. Our combined QA system achieves 9.3% increase in accuracy over GPT-3 and 40.3% increase over BERT QA. Thus, we infer that KG-DL performs better than either singly.
cs.CL↗
Gradient estimates for the Lagrangian mean curvature equation with critical and supercritical phase
In this paper, we prove interior gradient estimates for the Lagrangian mean curvature equation, if the Lagrangian phase is critical and supercritical and $C^{2}$. Combined with the a priori interior Hessian estimates proved in [Bha21, Bha22], this solves the Dirichlet boundary value problem for the critical and supercritical Lagrangian mean curvature equation with $C^0$ boundary data. We also provide a uniform gradient estimate for lower regularity phases that satisfy certain additional hypotheses.
math.AP↗
Rigidity for general semiconvex entire solutions to the sigma-2 equation
We show that every general semiconvex entire solution to the sigma-2 equation is a quadratic polynomial. A decade ago, this result was shown for almost convex solutions.
math.AP↗
A Deep-Bayesian Framework for Adaptive Speech Duration Modification
We propose the first method to adaptively modify the duration of a given speech signal. Our approach uses a Bayesian framework to define a latent attention map that links frames of the input and target utterances. We train a masked convolutional encoder-decoder network to produce this attention map via a stochastic version of the mean absolute error loss function; our model also predicts the length of the target speech signal using the encoder embeddings. The predicted length determines the number of steps for the decoder operation. During inference, we generate the attention map as a proxy for the similarity matrix between the given input speech and an unknown target speech signal. Using this similarity matrix, we compute a warping path of alignment between the two signals. Our experiments demonstrate that this adaptive framework produces similar results to dynamic time warping, which relies on a known target signal, on both voice conversion and emotion conversion tasks. We also show that our technique results in a high quality of generated speech that is on par with state-of-the-art vocoders.
eess.AS↗
Non-parallel Emotion Conversion using a Deep-Generative Hybrid Network and an Adversarial Pair Discriminator
We introduce a novel method for emotion conversion in speech that does not require parallel training data. Our approach loosely relies on a cycle-GAN schema to minimize the reconstruction error from converting back and forth between emotion pairs. However, unlike the conventional cycle-GAN, our discriminator classifies whether a pair of input real and generated samples corresponds to the desired emotion conversion (e.g., A to B) or to its inverse (B to A). We will show that this setup, which we refer to as a variational cycle-GAN (VC-GAN), is equivalent to minimizing the empirical KL divergence between the source features and their cyclic counterpart. In addition, our generator combines a trainable deep network with a fixed generative block to implement a smooth and invertible transformation on the input features, in our case, the fundamental frequency (F0) contour. This hybrid architecture regularizes our adversarial training procedure. We use crowd sourcing to evaluate both the emotional saliency and the quality of synthesized speech. Finally, we show that our model generalizes to new speakers by modifying speech produced by Wavenet.
eess.AS↗
Multi-speaker Emotion Conversion via Latent Variable Regularization and a Chained Encoder-Decoder-Predictor Network
We propose a novel method for emotion conversion in speech based on a chained encoder-decoder-predictor neural network architecture. The encoder constructs a latent embedding of the fundamental frequency (F0) contour and the spectrum, which we regularize using the Large Diffeomorphic Metric Mapping (LDDMM) registration framework. The decoder uses this embedding to predict the modified F0 contour in a target emotional class. Finally, the predictor uses the original spectrum and the modified F0 contour to generate a corresponding target spectrum. Our joint objective function simultaneously optimizes the parameters of three model blocks. We show that our method outperforms the existing state-of-the-art approaches on both, the saliency of emotion conversion and the quality of resynthesized speech. In addition, the LDDMM regularization allows our model to convert phrases that were not present in training, thus providing evidence for out-of-sample generalization.
eess.AS↗
Analysis of Selective-Decode and Forward Relaying Protocol Over kappa-mu Fading Channel Distribution
In this work, we examine the performance of selective-decode and forward (S-DF) relay systems over kappa-mu fading channel condition. We discuss about the probability density function (PDF), system model, and cumulative distribution function (CDF) of kappa-mu distributed envelope and signal to noise ratio (SNR) and the techniques to generate samples that follow kappa-mu distribution. Specifically, we consider the case where the source-to-relay (SR), relay-to-destination (RD) and source-to-destination (SD) link is subject to the independent and identically distributed (i.i.d.) kappa-mu fading. From the simulation results, the enhancement in the symbol error rate (SER) with a stronger line of sight (LOS) component is observed. This shows that S-DF relaying systems can perform well even in the non-fading or LOS conditions. Monte Carlo simulations are conducted for various values of fading parameters and the outcomes closely match with theoretical outcomes which validate the derivations.
cs.NI↗
Regularity for convex viscosity solutions of special Lagrangian equation
We establish interior regularity for convex viscosity solutions of the special Lagrangian equation. Our result states that all such solutions are real analytic in the interior of the domain.
math.AP↗
Hessian estimate for semiconvex solutions to the sigma-2 equation
We derive a priori interior Hessian estimates for semiconvex solutions to the sigma-2 equation. An elusive Jacobi inequality, a transformation rule under the Legendre-Lewy transform, and a mean value inequality for the still nonuniformly elliptic equation without area structure are the key to our arguments. Previously, this result was known for almost convex solutions.
math.AP↗
Recovering a quasilinear conductivity from boundary measurements
We consider the inverse problem of recovering an isotropic quasilinear conductivity from the Dirichlet-to-Neumann map when the conductivity depends on the solution and its gradient. We show that the conductivity can be recovered on an open subset of small gradients, hence extending a partial result to all real analytic conductivities. We also recover non-analytic conductivities with additional growth assumptions along large gradients. Moreover, the results hold for non-homogeneous conductivities if the non-homogeneous part is assumed known.
math.AP↗
Quasi-Noether systems and quasi-Lagrangians
We study differential systems for which it is possible to establish a correspondence between symmetries and conservation laws based on Noether identity: quasi-Noether systems. We analyze Noether identity and show that it leads to the same conservation laws as Lagrange (Green-Lagrange) identity. We discuss quasi-Noether systems, and some of their properties, and generate classes of quasi-Noether differential equations of the second order. We next introduce a more general version of quasi-Lagrangians which allows us to extend Noether theorem. Here, variational symmetries are only sub-symmetries, not true symmetries. We finally introduce the critical point condition for evolution equations with a conserved integral, demonstrate examples of its compatibility, and compare the invariant submanifolds of quasi-Lagrangian systems with those of Hamiltonian systems.
math-ph↗
A Big data analytical framework for portfolio optimization
With the advent of Web 2.0, various types of data are being produced every day. This has led to the revolution of big data. Huge amount of structured and unstructured data are produced in financial markets. Processing these data could help an investor to make an informed investment decision. In this paper, a framework has been developed to incorporate both structured and unstructured data for portfolio optimization. Portfolio optimization consists of three processes: Asset selection, Asset weighting and Asset management. This framework proposes to achieve the first two processes using a 5-stage methodology. The stages include shortlisting stocks using Data Envelopment Analysis (DEA), incorporation of the qualitative factors using text mining, stock clustering, stock ranking and optimizing the portfolio using heuristics. This framework would help the investors to select appropriate assets to make portfolio, invest in them to minimize the risk and maximize the return and monitor their performance.
q-fin.GN↗
Outage Probability Analysis of Selective-Decode and Forward Cooperative Wireless Network over Time Varying Fading Channels with Node Mobility and Imperfect CSI Condition
In this work, we explore the outage probability (OP) analysis of selective decode and forward (SDF) cooperation protocol employing multiple-input multipleoutput (MIMO) orthogonal space-time block-code (OSTBC) over time varying Rayleigh fading channel conditions with imperfect channel state information (CSI) and mobile nodes. The closed-form expressions of the per-block average OP, probability distribution function (PDF) of sum of independent and identically distributed (i.i.d.) Gamma random variables (RVs), and cumulative distribution function (CDF) are derived and used to investigate the performance of the relaying network. A mathematical framework is developed to derive the optimal source-relay power allocation factors. It is shown that source node mobility affects the per-block average OP performance more significantly than the destination node mobility. Nevertheless, in other node mobility situations, cooperative systems are constrained by an error floor with a higher signal to noise ratio (SNR) regimes. Simulation results show that the equal power allocation is the only possible optimal solution when source to relay link is stronger than the relay to destination link. Also, we allocate almost all the power to the source node when source to relay link is weaker than the relay to destination link. Simulation results also show that OP simulated plots are in close agreement with the OP analytic plots at high SNR regimes.
cs.NI↗
PEP Analysis of Selective Decode and Forward Protocol over Keyhole Fading
We provide a closed form upper bound formulation for the average pairwise-error probability (PEP) of selective decode and forward (SDF) cooperation protocol for a keyhole (pinhole) channel condition. We have employed orthogonal space-time block-code scheme (OSTBC) in conjunction with multi-antenna (MIMO) technology. We have used moment generating function (MGF) based approach for deriving the upper bound of PEP. PEP expression provides information regarding the performance of the wireless system with respect to the channel conditions. We have included simulation results which confirm the analytical results of our proposed upper bound. Simulation results show that due to keyhole effect performance of wireless system degrades.
cs.NI↗
An inverse problem from condense matter physics
We consider the problem of reconstructing the features of a weak anisotropic background potential by the trajectories of vortex dipoles in a nonlinear Gross-Pitaevskii equation. At leading order, the dynamics of vortex dipoles are given by a Hamiltonian system. If the background potential is sufficiently smooth and flat, the background can be reconstructed using ideas from the boundary and the lens rigidity problems. We prove that reconstructions are unique, derive an approximate reconstruction formula, and present numerical examples.
math.AP↗